In this paper, we propose a new sixth-order weighted essentially non-oscillatory (WENO) scheme for solving compressible aerodynamics. As with the previous six-order central upwind WENO scheme, this present scheme is a convex combination of four linear reconstructions. The stencil type is the same as WENO-Z6 scheme (Hu FX 2018), although the first three upwind stencils nominally use three cell values, the original secondary reconstruction has been modified to have fourth-order accuracy by adding a third-order correction term involving five cell values. In addition, corresponding smoothness indicators are provided, the new schemes are called WENO-MS-JS6 and WENO-MS-Z6. And by using the new reference smoothness indicator, the WENO-MS-Z6 scheme achieved the optimal convergence accuracy order in the smooth region including the first-order critical point ( \(f^\prime _i=0,f^{\prime \prime }_i \ne 0, f^{\prime \prime \prime }_i \ne 0 \) ). Several numerical examples demonstrate that the new schemes have better resolution and the same robustness as the recently developed sixth order WENO schemes.
